Local constrained controllability problems for nonlinear finite-dimensional discrete 1-D and 2-D control systems with constant coefficients are formulated and discussed. Using some mapping theorems taken from nonlinear functional analysis and linear approximation methods, sufficient conditions for constrained controllability in bounded domains are derived and proved. The paper extends the controllability conditions with unconstrained controls given in the literature to cover both 1-D and 2-D nonlinear discrete systems with constrained controls.
@article{bwmeta1.element.bwnjournal-article-amcv12i2p173bwm,
author = {Klamka, Jerzy},
title = {Controllability of nonlinear discrete systems},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {12},
year = {2002},
pages = {173-180},
zbl = {1017.93014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv12i2p173bwm}
}
Klamka, Jerzy. Controllability of nonlinear discrete systems. International Journal of Applied Mathematics and Computer Science, Tome 12 (2002) pp. 173-180. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv12i2p173bwm/
[000] Graves L.M. (1950): Some mapping theorems. - Duke Math.J., Vol. 17, No.1, pp. 111-114. | Zbl 0037.20401
[001] Kaczorek T. (1985): Two-Dimensional Linear Systems. - Berlin: Springer. | Zbl 0593.93031
[002] Kaczorek T. (1993): Linear Control Systems. - New York: Wiley. | Zbl 0784.93003
[003] Kaczorek T. (1995): U-reachability and U-controllability of 2-D Roesser model. - Bull. Polish Acad. Sci. Tech. Sci., Vol. 43, No. 1, pp. 31-37. | Zbl 0849.93010
[004] Klamka J. (1988a): M-dimensional nonstationary linear discrete systems in Banach spaces. - Proc. 12-th IMACS World Congress, Paris, Vol. 4, pp. 31-33.
[005] Klamka J. (1988b): Constrained controllability of 2-D linear systems. - Proc. 12-th IMACS World Congress, Paris, Vol. 2, pp. 166-169.
[006] Klamka J. (1991a): Complete controllability of singular 2-D system. - Proc. 13-th IMACS World Congress, Dublin, pp. 1839-1840.
[007] Klamka J. (1991b): Controllability of Dynamical Systems. -Dordrecht: Kluwer. | Zbl 0732.93008
[008] Klamka J. (1992): Controllability of nonlinear 2-D systems. - Bull.Polish Acad. Sci. Tech. Sci., Vol. 40, No. 2, pp. 125-133. | Zbl 0767.93004
[009] Klamka J. (1993): Controllability of dynamical systems-A survey. - Arch.Contr. Sci., Vol. 2, No. 3, pp. 281-307. | Zbl 0818.93002
[010] Klamka J. (1994): Constrained controllability of discrete 2-D linear systems. - Proc. IMACS Int. Symp. Signal Processing, Robotics and Neural Networks, Lille, France, pp. 166-169.
[011] Klamka J. (1995): Constrained controllability of nonlinear systems. - IMA J. Math. Contr. Inf., Vol. 12, No. 2, pp. 245-252. | Zbl 0840.93014
[012] Klamka J. (1996): Controllability of 2-D nonlinear systems. - Proc.2-nd World Congress Nonlinear Analysis, Athens, Greece, pp. 196-199.
[013] Robinson S.M. (1986): Stability theory for systems of inequalities. Part II: Differentiable nonlinear systems. - SIAM J. Numer. Anal., Vol. 13, No. 4, pp. 1261-1275.